Internal Hydraulic Jumps with Upstream Shear

Kelly Ogden, Ph.D., 2017Karl Helfrich, Advisor

Internal hydraulic jumps in flows with upstream shear are investigated numerically and theoretically. The role of upstream shear has not previously been thoroughly investigated, although it is important in many oceanographic flows such as exchange flows and stratified flow over topography. Several two-layer shock joining theories are considered and extended to include upstream shear, entrainment, and topography. Theoretical results are also compared to 2D and some 3D numerical simulations of the full Navier-Stokes equations, which allow continuous velocity and density distributions.

The solution space of idealized jumps with small upstream shear is identified using two-layer theories, which shows that upstream shear allows larger jumps to form and allows jumps for a larger range of parameters. Numerical simulations reveal several jump structures that can occur. At low shear, the 2D mixing efficiency is constant across simulations. As shear increases, the basic two-layer theories no longer provide solutions. Numerical simulations show that entrainment and continuous velocity profiles become significant as the shear increases. The 2D mixing efficiency also decreases significantly as shear increases. Finally, more realistic 2D and some 3D simulations including topography bridge the gap between the highly idealized simulations and the very realistic work of others.